Let a = 12 - 3 + 13 - 8 + 14 - 15 then we have

Answer: Option A

$$\begin{array}{rl}& a=\frac{1}{2-\sqrt{3}}+\frac{1}{3-\sqrt{8}}+\frac{1}{4-\sqrt{15}}\\ & \Rightarrow \frac{1}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}+\frac{1}{3-\sqrt{8}}\times \frac{3+\sqrt{8}}{3+\sqrt{8}}+\frac{1}{4-\sqrt{15}}\times \frac{4+\sqrt{15}}{4+\sqrt{15}}\\ & \Rightarrow \frac{2+\sqrt{3}}{4-3}+\frac{3+\sqrt{8}}{9-8}+\frac{4+\sqrt{15}}{16-15}\\ & \Rightarrow 2+\sqrt{3}+3+\sqrt{8}+4+\sqrt{15}\\ & \Rightarrow 9+\sqrt{3}+2\sqrt{2}+\sqrt{15}\\ & a=9<9+\sqrt{3}+2\sqrt{2}+\sqrt{15}<18\\ & \sqrt{3}=1.73,\sqrt{2}=1.41,\sqrt{15}=3.9\\ & \Rightarrow 9<9+1.73+\left(2\times 1.41\right)+3.9=17.4<18\end{array}$$